Further to my question on the usage of “workingest” in the Time magazine’s article (November 14), “Whatever happened to upward mobility,” I noticed the word “inflection point,” in the following sentence in the same article:

“International Monetary Fund research shows that countries like the U.S. and U.K. are more prone to boom and bust cycles. And they are ultimately at risk for social instability. That the inflection point that we are at right now.”

I am not clear with meaning of “inflection point” and the difference of it from other resembling expressions, such as “turning point,” “diverging point,” "bifurcation" or “junction.”

Apart from a bookish mathematical definition of the inflection points as “the point where the function changes concavity” with an example equation, “f(x) = x3”, which I found in www.clas.usb. edu, what does “inflection point” mean in the contest of the above sentence?

The sense in which the mathematical term inflection point can be applied to something like economics is the point at which things change from getting better to getting worse or the other way around. This is not the same as going from good to bad (or bad to good). This is about the rate of change of movement going from positive to negative or vice versa.

A turning point could be an inflection point, but it could also refer to a sudden change. Inflection points are generally gradual. Also, there is nothing about a turning point that implies that things will be going in the opposite direction, whereas inflection points do have that kind of implication.

Diverging and junctions have to to with separating and rejoining two paths, whereas both inflection points and turning points refer to single paths.